The Calculus of One-Sided \(M\)-Ideals and Multipliers in Operator Spaces

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David P. Blecher; Vrej Zarikian

The theory of one-sided \(M\)-ideals and
multipliers of operator spaces is simultaneously a generalization of classical
\(M\)-ideals, ideals in operator algebras, and aspects of the theory of
Hilbert \(C^*\)-modules and their maps. Here we give a systematic
exposition of this theory. The main part of this memoir consists of a
‘calculus’ for one-sided \(M\)-ideals and multipliers, i.e.
a collection of the properties of one-sided \(M\)-ideals and
multipliers with respect to the basic constructions met in functional analysis.
This is intended to be a reference tool for ‘noncommutative functional
analysts’ who may encounter a one-sided \(M\)-ideal or multiplier
in their work.

Title (HTML):
The Calculus of One-Sided \(M\)-Ideals and Multipliers in Operator Spaces

Author(s) (Product display):
David P. Blecher;
Vrej Zarikian

Affiliation(s) (HTML):
University of Houston, Houston, TX;
University of Cincinnati, Cincinnati, OH

Abstract:

The theory of one-sided \(M\)-ideals and
multipliers of operator spaces is simultaneously a generalization of classical
\(M\)-ideals, ideals in operator algebras, and aspects of the theory of
Hilbert \(C^*\)-modules and their maps. Here we give a systematic
exposition of this theory. The main part of this memoir consists of a
‘calculus’ for one-sided \(M\)-ideals and multipliers, i.e.
a collection of the properties of one-sided \(M\)-ideals and
multipliers with respect to the basic constructions met in functional analysis.
This is intended to be a reference tool for ‘noncommutative functional
analysts’ who may encounter a one-sided \(M\)-ideal or multiplier
in their work.